I'd like to have an algorithm for computing the ring of invariants of a reductive group (i.e. G acts on V, compute C[V]^G). I know that there are algorithms in existance for this, e.g. see http://www.math.lsa.umich.edu/~hderksen/Publications/invar1999.pdf. Does anyone know if this has been implemented in Maple, or where to find code in another language? Any ideas on what sort of data structure would be appropriate

The scale of vertical axis is logarithmic and function in each interval must be linear. When I use the command " mode=log " the shape of lines are deformed into curves, however when I use the command " curve ", the shape of lines remains straight. I can use right-click for changing mode to logarithmic scale but is it possible to use label font for vertical axis as well as size, resolution and other options in the command "curve" ?

Thanks alot

restart; with(plottools):

SN := curve([[3, (4.566256-4.544647)/(4.544647)], [4, (4.544933-4.544647)/(4.544647)], [5, (4.544653-4.544647)/(4.544647)], [6, (4.544649-4.544647)/(4.544647)], [7, 0]]): PLOT(SN);

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for m to 5 do

x[m] := m+2 end do:

y[1, 1] := (4.566256-4.544647)/(4.544647):y[2, 1] := (4.544933-4.544647)/(4.544647): y[3, 1] := (4.544653-4.544647)/(4.544647): y[4, 1] := (4.544649-4.544647)/(4.544647): y[5, 1] := 0:

for j to 1 do for i to 4 do

L[i, j] := (y[i+1, j]-y[i, j])*(x-x[i])+y[i, j] end do:

PW[j] := piecewise(`and`(x >= x[1], x < x[2]), L[1, 1], `and`(x >= x[2], x < x[3]), L[2, 1], `and`(x >= x[3], x < x[4]), L[3, 1], `and`(x >= x[4], x < x[5]), L[4, 1]) end do:

plot(PW[1], x = x[1] .. x[5], color = black, axes = framed, font = [Times, 13], size = [650, 550], resolution = 1200, legendstyle = [location = top], legend = ['gamma' = -.4], linestyle = solid, thickness = 2, labels = [Number*of*Basis, '(P-P[min])/P[min]'], labelfont = [Times, 13], axis[2] = [mode = log]);

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Hi friends! I have a problem with Random Variable. I don't understand why theoretical Mean differs from sample's Mean

restart; with(Statistics);

r := RandomVariable(NegativeBinomial(3, .1));
Mean((3-1)/(3+r-1));

0.1000000000

S := Sample(r, 10000);

d := map(unapply((3-1)/(3+t-1), t), S);

Mean(d);

0.04703520901756091

But !!

For example if p=0.2 then all is well

Hi there, 

I'm trying to find a way to find the Preimage for a single point (or a small set) of a complex rational function. I've tried with the command RationalMapPreimage, which sounds like the thing to try, but I can't get my head around how this command works?

(For context, I'm trying to find the preimages of a the fixed/critical/postcritial points of a function something like f(z)=(z²-1)/(z²+1))

Many Thanks

I try to make a question with an equation with numbered variables. This works fine when evaluating:

y=x1/x2

I need to have the lefthand variable indexed also like this:

y2=x1/x2

When entering y2=x1/x2 as the answer Maple TA won't evaluate it as a correct answer!?

I have the following code:

restart;
PDE := diff(u(x, t), t) = diff(u(x, t), x, x)-sin(x+t)+cos(x+t);
IBC:= D[1](u)(0,t)=-sin(t),
D[1](u)(1,t)=-(u(1, t))^4+(cos(1+t))^4-sin(1+t),
u(x,0)=cos(x);

pds := pdsolve( PDE, [IBC], numeric, time = t, range = 0 .. 1,

spacestep = 0.1e-1, timestep = 0.1e-1,
errorest=true
)

And I want to plot the difference |pds(t,x) - cos(x+t)| in maple for x=1 and t=0..5

I thought to use the following piece of commands but I get an error:

P:=unapply(pds, t,x);
Q:=abs(P(t,x)-cos(x+t));
Q:-plot(x=1, t=0..1);

I get an error that Q isn't a module.

I thought that unapply is used for this case, can you help me with this simple task?

Thanks in advance.

Hi

Im trying to make a small maple document, where i can calculate the moecule mass of any molecule. I want to assign all atoms with a value for its atom mass, but it will not let me unassign I, as this is the standard unit for imaginary numbers. Is there any way i can unassign I and give it a new value just in the current instance of the program? I dont want it to unassign I in other documents.

Thank you in advance

Hi all

I have this repetition with for:

for i from 1 to 10000 do x[i]:=sqrt(i); print(i); end do:

I want to know at the same time when the repetition is working, the value of i where the calculation is. Not at the last time of the calculation of all the repititions.

Example: when i=1, I want to see 1, when i=600, I want to see 600 at the same time of execution the repetition and not the last of the repetition  

Thank you

f := x^4-c1*x^3+c2*x^2-c3*x+c4;

restart;
ferrai := -x1^3*x2*x3*x4-x1^2*x2^2*x3^2-x1^2*x2^2*x4^2-x1^2*x3^2*x4^2-x1*x2^3*x3*x4-x1*x2*x3^3*x4-x1*x2*x3*x4^3-x2^2*x3^2*x4^2+x1^2*x2*x3*y+x1^2*x2*x4*y+x1^2*x3*x4*y+x1*x2^2*x3*y+x1*x2^2*x4*y+x1*x2*x3^2*y+x1*x2*x4^2*y+x1*x3^2*x4*y+x1*x3*x4^2*y+x2^2*x3*x4*y+x2*x3^2*x4*y+x2*x3*x4^2*y-x1*x2*y^2-x1*x3*y^2-x1*x4*y^2-x2*x3*y^2-x2*x4*y^2-x3*x4*y^2+y^3;
coeff(ferrai, y^3);
coeff(ferrai, y^2);
coeff(ferrai, y);
res := ferrai - coeff(ferrai, y^3)*y^3 - coeff(ferrai, y^2)*y^2 - coeff(ferrai, y)*y;

c2 := -coeff(ferrai, y^2)/coeff(ferrai, y^3);
sys1 := c1*c3 - 4*c4 = coeff(ferrai, y)/coeff(ferrai, y^3);
sys2 := -c3^2-(c1^2)*c4+4*c2*c4 = res;
solve([sys1, sys2],[c1,c3,c4]);

number of equations is not enough, is it possible to find back c1,c3,c4?

though c2 is easy to know

assume not starting from resolvent of quartic,

how to find [[1,2],[3,4]] and [[1,3],[2,4]] and [[1,4],[2,3]] ?

a1*a2 + a3*a4 if [[1,3,2,4],[1,2]]

a1*a3 + a2*a4 if [2,3][[1,3,2,4],[1,2]]

a1*a4 + a2*a3 if [2,4],[[1,3,2,4],[1,2]]

moreover, i use multiplication of permutation group can not multiply below

though i know how to operate multiplication by hand, i follow the syntax to do multiplication, seems not the way

with(group):
mulperms([[2,3]], [[1,3,2,4],[1,2]]);
mulperms([[1,3,2,4],[1,2]], [[2,3]]);

mulperms([2,3], [[1,3,2,4],[1,2]]);
mulperms([[1,3,2,4],[1,2]], [2,3]);

how to find [[1,3,2,4],[1,2]] and [2,3][[1,3,2,4],[1,2]] and [2,4],[[1,3,2,4],[1,2]]?

and why Orbits(G) put permutation group into power, how to display the result of this power group?

i use this or quartic polynomials' resolvent

with(GroupTheory):
G := SpecialUnitaryGroup(3, 1);
Orbits(G);
Orbit(1,G);
Orbit(3,G);

So im trying to solve multiple ODES using dsolve(numeric) but I jsut cant get it to work.

I kep getting this one error: 

Error, (in f) unable to store '-HFloat(0.020918994979034728)-HFloat(0.09184018333019917)*I' when datatype=float[8]

This is my uploaded file 

(for some reason the uploaded file didnt show the error at the bottom so i just pasted it in the spot it would appear.

Download CHE504_HW5.mw

hi all

i have tow equations and i want plot q vs.A , that A change beetwin 0..phi. vn and a are definite and positive.

plz plz help me

(diff(f,y))^2-(f[y]^4)/4+q^2/(f[y]^2)+(1+2*q^2)*(f[y]^2)/2=piecewise(y<-a,1/4+2*q^2,-a<y<a,vn*(f[y]^2)-vn+1/4+2*q^2,y>a,1/4+2*q^2);

phiB[infinity]=q*int(f,y=-infinity..infinity):
A:=phiB[infinity]:

Hi

I have this attched procedure "Alt_lisse1".

Why the result e1 does'nt take into account the known variables

Thanks

ALt_lisse1.mw

Hi

is it possible to remove this warning and not to show it when executing a procedure ? 

Warning, `AzIII` is implicitly declared local to procedure `lisse`

Thanks